Final answer:
The slope of the line passing through points (-7, 2.3) and (-7, 14.2) is undefined as the run (change in x) is zero, resulting in division by zero when calculating the slope.
Step-by-step explanation:
The slope of a line passing through two points can be found by the formula m = (y2 - y1) / (x2 - x1), where m is the slope, (x1, y1) and (x2, y2) are the coordinates of the two points. In this case, since the x-coordinates of the points (-7, 2.3) and (-7, 14.2) are the same, the run (x2 - x1) is zero. This results in the slope being undefined or infinite.
The formula for finding the slope given two points (x1, y1) and (x2, y2) is m = (y2 - y1) / (x2 - x1). Applying it to the points given, we calculate:
- (x1, y1) = (-7, 2.3)
- (x2, y2) = (-7, 14.2)
- Run (change in x) = x2 - x1 = -7 - (-7) = 0
- Rise (change in y) = y2 - y1 = 14.2 - 2.3 = 11.9
- Slope m = rise / run = 11.9 / 0 which is undefined
Thus, the slope is not defined and the correct answer is: a) Undefined or d) Infinite.